Physics - Fluid Question with Solution | TestHub

According to the equation of continuity, the volume flow rate of an incompressible fluid remains constant throughout the pipe.

$A_1{V}_1=A_2{V}_2$

Let the diameter of the nozzle be $d_1$. The cross-sectional area of the pipe is $A_1=\frac{\pi d^2}{4}$ and the cross-sectional area of the nozzle is $A_2=\frac{\pi d_1^2}{4}$.

Substituting the values into the equation of continuity:

$\frac{\pi d^2}{4}V=\frac{\pi d_1^2}{4}{V}_1$

$d^{2}V=d_1^2{V}_1$

$d_1^2=d^2\frac{V}{V_1}$

$d_1=d\sqrt{\frac{V}{V_1}}$

Answer: $\text{d}\sqrt{\frac{\text{V}}{{\text{V}}_1}}$